Legally, the "Made In England", or "London Made", or any variation thereof stamped on the side of a pipe are a guarantee of nothing more than that it was assembled in England.
The French created the briar pipe, not the British. French merchants set up companies in England to sell and distribute briar pipes made in France. Stamping the pipes as "made in England" gave them a more accepting local market.
To some degree, part of the manufacturing process was done in England, usually the finishing of the bowl and mounting with a stem. I would guess there was a tax advantage to importing components rather than finished goods.
Even after British companies began manufacturing their own pipes, they relied heavily on bowls and stems imported from France and Germany, only supplementing their stock with home made product. Regardless of where the bowl was turned, it was stamped with a "Made In England" or some variation stamp. Having that stamp gave the pipe a level of unmerited cachet given that the superior and more experienced carvers were to be found in France.
The importance of maintaining this fiction is underscored by a kerfuffle that took place in 1928 when Barling sought to amend provisions pertaining to briar pipes in the Merchandise Marks Act. Barling wanted it amended to require that pipes stamped with a "Made in England" or "Made In London" stamp, or any variation thereof, to actually be made in England, London, or etc. Barling was making all their own pipes, while their competitors were continuing to import sizeable portions of their stock from France. Barling felt that they deserved the prestige derived from that "Made in England" stamp. After all, they were actually making all their own pipes.
The rest of the pipe manufacturing industry closed ranks against them. According to the transcripts, Dunhill threatened to close up operations in England and move them off shore, Comoy stated flatly that the skills to properly turn bowls did not exist in England and could not be developed, etc.
In the end, Barling lost and so a bowl can be turned elsewhere and still be stamped as "Made In England" or "Made in London" or some such variable as long as the parts are put together in England.